Microlensed image centroid motions by an exotic lens object with negative convergence or negative mass

Gravitational lens models with negative convergence inspired by modified gravity theories, exotic matter and energy have been recently examined, in such a way that a static and spherically symmetric modified spacetime metric depends on the inverse distance to the $n$-th power ($n=1$ for Schwarzschild metric, $n=2$ for Ellis wormhole, and $n \neq 1$ for an extended spherical distribution of matter such as an isothermal sphere) in the weak-field approximation [Kitamura, Nakajima and Asada, PRD 87, 027501 (2013), Izumi et al. PRD 88 024049 (2013)]. Some of the models act as if a convex lens, whereas the others are repulsive on light rays like a concave lens. The present paper considers microlensed image centroid motions by the exotic lens models. Numerical calculations show that, for large $n$ cases in the convex-type models, the centroid shift from the source position might move on a multiply-connected curve like a bow tie, while it is known to move on an ellipse for $n=1$ case and to move on an oval curve for $n=2$. The distinctive feature of the microlensed image centroid may be used for searching (or constraining) localized exotic matter or energy with astrometric observations. It is shown also that the centroid shift trajectory for concave-type repulsive models might be elongated vertically to the source motion direction like a prolate spheroid, whereas that for convex-type models such as the Schwarzschild one is tangentially elongated like an oblate spheroid.